Question

Let θ  ∈ (0, π/2). If the system of linear equations

(1 + cos² θ)x + sin² θ y + 4 sin3 θ z = 0

cos²θ x + (1+sin²θ)y + 4 sin3 θ z = 0

cos²θ x + sin² θ y +(1+4 sin3 θ) z =0

has a non-trivial solution, then the value of θ is:

(1) \(\cfrac{4\pi}{9}\)

(2) \(\cfrac{7\pi}{18}\)

(3) \(\cfrac{\pi}{18}\)

(4) \(\cfrac{5\pi}{18}\)

Answer 1

Correct answer is: (2) \(\cfrac{7\pi}{18}\)